Here are my own favorite takeaway family tree research tips from
"Genealogy Roadshow":

Don't believe everything your family told you about your
ancestors. Whether it's the year Great-grandpa arrived in
the United States or a rumored link to George Washington, treat
family stories as theories that require research to prove or
disprove.

You can't get away from the "start with yourself and work
backward" principle. No matter what family claim the
"Genealogy Roadshow" experts were researching, the research
started with the present and moved to the person's parents, then
grandparents, etc. You didn't get details about every generation
in the show's quick segments (remember the entertainment factor), but those generations were listed
in the trees that flashed by.

You're related to lots of people. Among them is
probably someone famous and someone infamous (remember this next
time one of those announcements comes out about which
celebrities are related—it's really not anything unusual). The
way to document a connection between two people is to research
both family trees as you normally would, and find a person
common to both trees.

Build on others' work. "Genealogy Roadshow" sometimes
used already-existing, reliable research about famous folks.
Don't be afraid to look for clues in published family histories
and family trees you find online—just make sure you do research
to verify all the names, dates and relationships in those
resources, so you don't end up repeating someone else's mistakes
and claiming the wrong ancestors.

Once you get beyond your garden-variety first or second
cousin, figuring out exactly how you're related to someone can
seem complicated. The trick is to find the most recent
common ancestor to the two cousins in question. If there's a
different number of generations between each cousin and the most
recent common ancestor, the cousins are "removed." The number of
removes is equal to the number of generations that separates the
two cousins. We explain
cousin relationships here and have a free
relationship chart PDF download here.

Sometimes genealogical discoveries come quickly, and
sometimes it takes a lot of research to find answers. The
show's hosts often used the word "we" when talking about records
discovered. Behind the scenes, full-time, professional
researchers were devoting hours upon hours to tracing guests'
family trees. You might not be able to devote that much time at
once to your research, but keep plugging away a little bit at a
time. And keep track of what you've done so next time you can
pick up where you left off.